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If mean = 5, Standard deviation = 2.6, median = 5 and quartile deviatiion = 1.5, then the coefficient of quartile deviation equals.
- a)35
- b)39
- c)30
- d)32
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
If mean = 5, Standard deviation = 2.6, median = 5 and quartile deviati...
Coefficient of QD = QD ×100/median
So,. 1.5×100/5=30
Formula explanation:
Coefficient of QD=Q3-Q2/Q3+Q2
=Q3-Q2/2÷Q3+Q2/2 ie QD/Median
So,. 1.5×100/5=30
Formula explanation:
Coefficient of QD=Q3-Q2/Q3+Q2
=Q3-Q2/2÷Q3+Q2/2 ie QD/Median
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Community Answer
If mean = 5, Standard deviation = 2.6, median = 5 and quartile deviati...
Given parameters:
- Mean = 5
- Standard deviation = 2.6
- Median = 5
- Quartile deviation = 1.5
Formula for Quartile Deviation:
Quartile Deviation = (Q3 - Q1)/2
where Q1 and Q3 are the first and third quartiles respectively.
Formula for Coefficient of Quartile Deviation:
Coefficient of Quartile Deviation = (Quartile Deviation / Median) * 100
Calculating Q1 and Q3:
Since the median is given as 5, we can assume that there are an even number of observations in the dataset. Therefore, the median falls between the 2nd and 3rd observations.
- Median = 5
- Observation 2 = ?
- Observation 3 = ?
We can use the formula for the median to find out the values of observation 2 and observation 3.
Median formula: (n + 1) / 2
where n is the number of observations.
Substituting the values:
- Median = 5
- n = 4
Median = (4 + 1) / 2 = 2.5
Observation 2 is the 2nd observation in the dataset, which is less than the median.
Observation 3 is the 3rd observation in the dataset, which is greater than the median.
- Observation 2 = 4
- Observation 3 = 6
Now we can calculate Q1 and Q3 using the observations.
- Q1 = (Observation 2 + Observation 3)/2 = (4 + 6)/2 = 5
- Q3 = 2 * Median - Q1 = 2 * 5 - 5 = 5
Calculating Quartile Deviation:
Quartile Deviation = (Q3 - Q1)/2 = (5 - 5)/2 = 0
Calculating Coefficient of Quartile Deviation:
Coefficient of Quartile Deviation = (Quartile Deviation / Median) * 100
= (0 / 5) * 100
= 0
Therefore, the coefficient of quartile deviation is 0, which is not listed as an option. However, it's possible that there is an error in the question, or the values provided are not accurate.
- Mean = 5
- Standard deviation = 2.6
- Median = 5
- Quartile deviation = 1.5
Formula for Quartile Deviation:
Quartile Deviation = (Q3 - Q1)/2
where Q1 and Q3 are the first and third quartiles respectively.
Formula for Coefficient of Quartile Deviation:
Coefficient of Quartile Deviation = (Quartile Deviation / Median) * 100
Calculating Q1 and Q3:
Since the median is given as 5, we can assume that there are an even number of observations in the dataset. Therefore, the median falls between the 2nd and 3rd observations.
- Median = 5
- Observation 2 = ?
- Observation 3 = ?
We can use the formula for the median to find out the values of observation 2 and observation 3.
Median formula: (n + 1) / 2
where n is the number of observations.
Substituting the values:
- Median = 5
- n = 4
Median = (4 + 1) / 2 = 2.5
Observation 2 is the 2nd observation in the dataset, which is less than the median.
Observation 3 is the 3rd observation in the dataset, which is greater than the median.
- Observation 2 = 4
- Observation 3 = 6
Now we can calculate Q1 and Q3 using the observations.
- Q1 = (Observation 2 + Observation 3)/2 = (4 + 6)/2 = 5
- Q3 = 2 * Median - Q1 = 2 * 5 - 5 = 5
Calculating Quartile Deviation:
Quartile Deviation = (Q3 - Q1)/2 = (5 - 5)/2 = 0
Calculating Coefficient of Quartile Deviation:
Coefficient of Quartile Deviation = (Quartile Deviation / Median) * 100
= (0 / 5) * 100
= 0
Therefore, the coefficient of quartile deviation is 0, which is not listed as an option. However, it's possible that there is an error in the question, or the values provided are not accurate.
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If mean = 5, Standard deviation = 2.6, median = 5 and quartile deviatiion = 1.5, then the coefficient of quartile deviation equals.a)35b)39c)30d)32Correct answer is option 'C'. Can you explain this answer?
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